Unified filter bank for audio coding

ABSTRACT

A unified filter bank for use in encoding and decoding MPEG-1 audio data, wherein input audio data is encoded into coded audio data and the coded audio data is subsequently decoded into output audio data. The unified filter bank includes a plurality of filters, with each filter of the plurality of filters being a cosine modulation of a prototype filter. The unified filter bank is operational as an analysis filter bank during audio data encoding and as a synthesis filter bank during audio data decoding, wherein the unified filter bank is effective to substantially eliminate the effects of aliasing, phase distortion and amplitude distortion in the output audio data.

This invention relates to audio coding, and in particular to methods andapparatus for audio compression and decompression.

The Motion Picture Experts Group MPEG-1 audio compression algorithm isan International Organisation for Standardisation (ISO) standard forhigh fidelity audio compression. MPEG-1 offers a choice of threeindependent layers of compression. These layers provide a wide range oftradeoffs between CODEC (coder/decoder) complexity and compressed audioquality.

Layer I is the simplest layer and is best suited for bit rates above 128kbits/sec per channel. For example, Phillips Digital Compact Cassette(DCC) uses Layer I compression at 192 kbits/sec per channel. This layercontains the basic mapping of the digital audio input into 32 sub-bands,fixed segmentation to format the data into blocks, a psychoacousticmodel to determine the adaptive bit allocation, and quantising usingblock compounding and formatting.

Layer II is an enhancement of Layer I. It improves the codingperformance by coding data in larger groups. The layer has intermediatecomplexity and is targeted for bit rates around 128 kbits/s per channel.

Layer III is the most complex of the three layers, but offers the bestaudio quality, particularly at bit-rates around 64 kbits/sec. The LayerIII MPEG-1 CODEC incorporates the analysis filter bank of MPEG-1 Layer Iand compensates for its deficiencies by increasing the frequencyresolution by further processing its output using a Modified DiscreteCosine Transform (MDCT). The resultant hybrid system has relatively highcomplexity and a relatively high computational load. Further, the hybridsystem does not prevent or remove the effects of aliasing.

The analysis filter bank used in the Layer I algorithm is in fact foundin all three layers of MPEG-1 CODECs. The analysis filter bank and itsinverse (a synthesis filter bank) do not form a perfect reconstruction(PR) system. The 32 constant width bands do not accurately reflect theear's critical bands. The bandwidth is generally too wide for lowerfrequencies and as a consequence the number of quantisers cannot betuned specifically for the noise sensitivity within each band.

A prototype filter, the filter from which the filters of the analysisbank are cosine modulations, is an approximate spectral factor of an Mthband filter. It provides near perfect reconstruction (NPR). As such, theanalysis filter bank and its inverse do not have paraunitarycharacteristics, ie their respective transformations are not lossless.Therefore, even under high transmission-bandwidth conditions the systemsuffers audible degradation.

An MPEG-1 Layer I CODEC 1, shown in block diagram form in FIG. 1,generally comprises two sections, an encoder (also referred to as acoder) 2 and a decoder 4. The encoder 2 includes an analysis filter bank6 which receives input audio data and divides that input audio data intomultiple frequency sub-bands. Simultaneously, the input audio data isprocessed by a psychoacoustic model 8 that determines the ratio ofsignal energy to a masking threshold for each mentioned sub-band. A bitallocation section 3 receives signal-to-mask ratios from thepsychoacoustic model 8 and determines how to apportion the total numberof code bits available for the quantization of the sub-band signals inorder to minimise the audibility of quantisation noise. A bit streamformatting section 5 generally receives the representations of thequantized sub-bands and formats that data together with side informationto produce an encoded bit stream.

The decoder 4 receives the encoded bit stream and removes the sideinformation in a bit stream unpacking stage 7. The quantised sub-bandvalues are restored in an inverse quantisation stage 10, and the audiosignal reconstructed from the subband values in a synthesis filter bankstage 11. The synthesis filter bank II is essentially the inverse of theanalysis filter bank 6 employed in the encoder 2.

The Layer I analysis filter bank 6 and its respective inverse 11, shownin FIG. 2 are an integral part of each layer of MPEG-1. The analysisfilter bank 6 divides the audio signal into 32 equal width frequencysubbands; Each filter H_(k)(z) 22 of the analysis filter bank 6 is acosine modulation of a prototype filter (often called a window in thecontext of a transform coder). Although the prototype is linear phase,the analysis and synthesis filters, which are cosine modulations of theprototype, are not. The prototype filter is an approximate spectralfactor of an M^(th) band filter and thereby only provides Near PerfectReconstruction, as detailed for example in D. Koilpillai, P. P.Vaidyanathan. “A Spectral Factorization Approach to Pseudo QMF Design”.Proc. IEEE Intl. Symp. Circuits and Systems pp. 160-163, Singapore June1991.

A MPEG-1 Layer III CODEC achieves additional frequency resolution by theuse of a hybrid filter bank 30, represented in block diagram form inFIG. 3. In this case each sub-band 32 is further split into 18 frequencysub-bands 34 by use of an MDCT (Modified Discrete Cosine Transform). TheMDCT employs a windowing operation with window length of 36. An adaptivewindow switching technique may be employed when the system is exposed totransient conditions. Although MDCT originated from Lapped OrthogonalTransforms it can be shown to have a mathematically equivalentinterpretation as a filter bank, as explained hereinbelow.

A two-channel, ie M=2, analysis and synthesis system based on arbitraryfilter design would generally exhibit three types of errors:

aliasing;

amplitude distortion and

phase distortion

It is known that aliasing can be completely eliminated in such a systemby correct choice of synthesis filters. It was later shown that atwo-channel QMF (Quadrature Mirror Filter) with correctly designed FIRfilters can eliminate all three types of distortion in a filter bank. Asystem, that can eliminate the effects of aliasing, phase distortion andamplitude distortion, is known in the art as a perfect reconstructionsystem. The above mentioned techniques are described, for example, inSmith M. J. T. and Barnwell T. P. “A procedure for designing exactreconstruction filter banks for tree structured subband coders”; Proc.IEEE International Conference Acoustic, Speech and Signal, Processing,pp. 27.1.1-27.1.4 1984.

A Pseudo QMF technique was developed by Nussbaumer, H.J., (“Pseudo QMFfilter bank”, IBM Technical Disclosure Bulletin, Vol. 24, pp. 3081-3087,No. 1981), which provides a technique for approximate aliasingcancellation in M channel filter banks.

The general theory of Perfect Reconstruction in M channel filter bankswas developed by a number of authors. Vetterli and Vaidyanathanindependently showed that the use of polyphase components leads to aconsiderable simplification of the theory of perfect reconstruction. Atechnique for the design of M channel perfect reconstruction systemsbased on polyphase matrices with the so-called paraunitary (lossless)properties was developed by Vaidyanathan, and was detailed inVaidyanathan P. P., “Multirate Systems and Filter Banks” Prentice HallSignal Processing Series, 1992.

A particular class of M-channel filter banks which effect perfectreconstruction systems was developed by Malvar, Koilpillai andVaidyanathan, and Ramstad, with the property that all the analysis andsynthesis filters, of respective analysis and synthesis filter banks,were derived, starting from a prototype filter, by modulation.

Before the development of filter banks with paraunitary properties, someauthors had independently reported other techniques for perfect recoverysystems which work for the case where the temporal resolution, filterorder N, is constrained by N+1=2M (M is the decimation factor). One ofthese was the aforementioned Lapped Orthogonal Transform (LOT). Asimilar concept is used in the Layer III hybrid system 30, whichaccounts for the fact that the overlap (18) is half the window size(36), as previously mentioned. ALOT is equivalent, in the framework of amulti-rate system, to a filter bank with paraunitary properties andtherefore also exhibits the perfect reconstruction property.

In a paper prepared by Koilpillai and Vaidyananthan, (Koilpillai D. andVaidyananthan P. P., “Cosine-Modulated FIR Filter Banks satisfyingPerfect Reconstruction”, IEEE Transaction on Signal Processing, volSP-40, pp. 770-783, 1992), the necessary and sufficient condition on the2M polyphase components of a linear phase prototype filter of lengthN+1=2 mM (where m is an arbitrary positive integer) was prescribed suchthat the polyphase component matrix of the modulated filter waslossless. They used the losslessness of the analysis/synthesis system toimplement Perfect Reconstruction filter banks using the latticestructures described in Vaidyananthan P. P. and Hoang P, (“Latticestructures for optimal design and robust implementation of two-channelperfect reconstruction QMF banks”, IEEE Transaction on Acoustic, Speechand Signal Processing vol. ASSP-36, pp 81-94, 1988).

In 1996 Nguyen and Koilpillai, in their paper Nguyen T. Q. AndKoilpillai D., “The Theory and Design of Arbitrary Length cosinemodulated filter banks and wavelets, satisfying perfect reconstruction”,IEEE Transaction on Acoustic, Speech and Signal Processing vol. ASSP-44,pp 473-483, 1996, derived a perfect reconstruction system for the casewhere the filter length is N+1=2 mM+m₁.

The hybrid filter structure 30 shown in FIG. 3 (i.e. Polyphase 31+MDCT33) generally complicates the implementation of the filter, has a highcomputational load and therefore requires an excessive amount of memorytransfers. As a consequence, the hybrid structure 30 consumes a lot ofpower. Further, the Layer I filter bank does not provide a PerfectReconstruction System and even at high bit rates, audio signals sufferunnecessary degradation Also, as stated in Sporer T., Bradenburg K. andElder B., (“The use of multi rate filter banks for coding of highquality digital audio” EUSIPCO 1992), cascading the polyphase filterbank to the MDCT results in aliasing problems due to the frequencyresponse of the polyphase filters being originally designed fornon-cascaded applications.

It is desirable to alleviate the difficulties and short comingsassociated with the above-mentioned known solutions to audiocompression, or at least provide a useful alternative.

In accordance with the present invention there is provided an MPEG-1CODEC, including an encoder, where the encoder has means for effectingan analysis filter bank, and a decoder, where the decoder has means foreffecting a synthesis filter bark, wherein a unified filter bank is themeans for effecting the analysis filter bank and a functional inverse ofthe unified filter bank is the means for effecting the synthesis filterbank, wherein the unified filter bank includes a plurality of filters,where each filter of the plurality of filters is a cosine modulation ofa prototype filter, P₀(Z), wherein the prototype filter includes aplurality of polyphase components, G_(k)(Z), which substantially satisfythe following:

${{{{\overset{\sim}{G}}_{k}(z)}{G_{k}(z)}} + {{{\overset{\sim}{G}}_{M + k}(z)}{G_{M + k}(z)}}} = \frac{1}{2M}$where

G_(k)(z), for 0≦k≦M−1, are the polyphase components of the prototypefilter,

{tilde over (G)}_(k)(z) is the conjugate transpose of G_(k)(z);

M is the decimation factor of the prototype filter, and

k is an integer.

In accordance with the present invention there is also provided a methodfor encoding and decoding audio data in a MPEG-1 Layer III CODEC whereininput audio data is encoded into coded audio data and said coded audiodata is decoded into output audio data, including subjecting the inputaudio data to an analysis filter bank during encoding, and a synthesisfilter bank during decoding, wherein a unified filter bank comprises theanalysis filter bank and a functional inverse of the unified filter bankcomprises the synthesis filter bank, the unified filter bank including aplurality of filters, where each filter of the plurality of filters is acosine modulation of a prototype filter, P₀(Z), wherein:

the temporal resolution, N, of the prototype filter is substantiallyN+1=1632;

the decimation factor, M, of the prototype filter is substantiallyM=576;

the bandwidth of the prototype filter is substantially π/M; and

the prototype filter substantially satisfies the following constraint:

${{{{\overset{\sim}{G}}_{k}(z)}{G_{k}(z)}} + {{{\overset{\sim}{G}}_{M + k}(z)}{G_{M + k}(z)}}} = \frac{1}{2M}$

Where, G_(k)(Z), for 0 ≦k ≦M−1, are the polyphase components of theprototype filter; G _(k)(z) is the conjugate transpose of G_(k)(z); andk is an integer.

The invention is flyer described by way of example only with referenceto the accompanying drawings, in which:

FIG. 1 is a block diagram of an MPEG-1 Layer I CODEC;

FIG. 2 is a block diagram of a decomposition of an analysis filter bankand a synthesis filter bank in MPEG-1 layer I CODEC;

FIG. 3 is a block diagram of a hybrid analysis system in an MPEG-1 LayerIII CODEC;

FIG. 4 shows the temporal resolution of MPEG-1 Layer III hybrid analysisfilter bank; and

FIG. 5 shows the magnitude response of the modulated filters Q_(k)(z) inaccordance with the invention.

An embodiment of the invention provides a unified analysis (andsynthesis) filter bank which has the same temporal resolution, N, andfrequency selectivity (sub-band width) as the above-described hybridsystem of a MPEG-1 Layer III CODEC. It is therefore useful to determinethe specification for the hybrid system 30, which may be examined withreference to the temporal resolution of MPEG-1 Layer III hybrid filterbank 40, diagrammatically illustrated in FIG. 4.

In FIG. 4, audio samples 42 are time labelled as x₀, x₁, . . . . Onlyevery 64^(th) sample is labelled for clarity. Each polyphase filterH_(k)(Z) 44, has filter length of 512, Sub-band values 46 of H_(k)(Z) 44are labelled x_(k,0), x_(k,1), . . . . Since the decimation factor ofthe Layer I analysis filter bank is equal to 32, the filter shifts by 32samples before convoluting and generating the next output 43.

The MDCT 33 has a prototype filter length of 36. C_(k,m)(z) 48 refers tothe m^(th) MDCT filter which takes input from H_(k)(z) 44. From FIG. 4,it can be seen that the temporal resolution 47 of the combined system is1632, ie 32*35+512=1632.

From FIG. 4 the decimation factor, M, for the overall system can be seento be 576, indicated by reference numeral 45. This value is equivalentto the product of the decimation factors of the two stages of the hybridsystem 30 ie the Layer I analysis filter bank and the MDCT, i.e.32*18=576.

The bandwidth of each Layer I filter, H_(k)(Z) 44, is π/M=π/32. Theresulting sub-band values 46 of the Layer I filters H_(k)(Z) are furtherdecomposed by into 18 sub-band values 34, for example. Therefore, thecombined band-width for each output of the hybrid system 30 isπ/(32*18)=π/(576).

In this example of the invention a perfect reconstruction system withprototype filter length N+1=1632, decimation factor M=576 and cut-offbandwidth of π/(M)=π/576 can replace the MPEG-1 Layer III hybrid systemwithout affecting other operations of the CODEC.

An example of the unified filter bank, perfect reconstruction system, ofthe present invention is described with reference to the derivation ofthe perfect reconstruction system, for the case where the filter lengthis N+1=2 mM+m₁, as referred to above.

Construction of a perfect reconstruction filter bank is defined by wayof an evolution from the Pseudo QMF (with near perfect reconstruction).Accordingly, consider a uniform DFT (Discrete Fourier Transform)analysis bank with 2M filters that are related according to:P _(k)(z)=P ₀(zW ^(k))  (1)i.e.,p _(k)(n)=p ₀(n)W ^(−kn)  (2)where P₀(z) is a prototype filter.

The impulse response is real, such that |P₀(e^(−jω))| is symmetric aboutω=0. The polyphase components of the prototype P₀(z) are G_(k)(z),0≦k≦2M−1, ie:

$\begin{matrix}{{P_{0}(z)} = {\sum\limits_{k = 0}^{{2M} - 1}\left\lbrack {z^{- k}{G_{k}\left( z^{2M} \right)}} \right\rbrack}} & (3)\end{matrix}$

The set of 2M responses are right shifted in order to make all thefilter bandwidths equal after combining negative and positive pairs. Thenew filters are given by:Q _(k)(z)=P ₀(zW ^(k+0.5))  (4)where

-   -   W=W_(2M)=e^(−j2π/2M)

The magnitude responses of Q_(k)(Z) and Q_(2M−1−k)(z), shown at 50 inFIG. 5, are now images of each other about ω=0, i.e. |Q_(k)(e^(−jω))|and |Q_(2M−1−k)(e^(−jω))|.

Accordingly, let:

$\begin{matrix}{{U_{k}(z)} = {c_{k}{P_{0}\left( {zW}^{k + 0.5} \right)}}} & (5) \\{\mspace{59mu}{{= {c_{k}{Q_{k}(z)}}}\mspace{11mu}{and}}} & (6) \\{{V_{k}(z)} = {c_{k}^{*}{P_{0}\left( {zW}^{- {({k + 0.5})}} \right)}}} & (7) \\{\mspace{56mu}{= {c_{k}^{*}{Q_{{2M} - 1 - k}(z)}}}} & (8)\end{matrix}$The M analysis filter banks can now be regarded as:H _(k)(z)=a _(k) U _(k)(z)+a _(k) *V _(k)(z), 0≦k≦M−1  (9)where

-   -   a_(k) and c_(k) are unit magnitude constants;    -   * denotes the conjugation of the respective coefficients; and    -   W=W_(2M)=e^(−j2π/2M)

The decimated output of the analysis filter banks, H_(k)(z), gives riseto alias components:H _(k)(zW _(M) ^(I))X _(k)(zW _(M) ^(I)), for all I  (10)

A synthesis filter F_(k)(Z), whose passband coincides with that of theanalysis filter, H_(k)(z), retains the unshifted versionH_(k)(z)X_(k)(z), and also permits a small leakage of the shiftedversions. In accordance with Pseudo QMF philosophy, the filters are alldesigned in such a way that when the output of all the M synthesisfilters are added together, the leakage (aliasing) are all mutuallycancelled. Since the passbands of the synthesis filter, F_(k)(z), shouldcoincide with those of the analysis filter, H_(k)(z), we are able toderive:F _(k)(z)=b _(k) U _(k)(z)+b* _(k) V _(k)(z), 0≦k ≦M−1  (11)where b_(k) is a unit magnitude constant.

In general, the output of F_(k)(z) has the aliasing components:H _(k)(zW ^(l) _(M))X _(k)(zW ^(l) _(M)), for all l i.e. 0≦k≦M−1  (12)

However, if the stopband attenuation of F_(k)(z) is sufficiently high,only some of these components are of importance. Consequently, in theNear Perfect Reconstruction case only those components are designed forcancellation. This leads to the constraint:a _(k) b* _(k) =−a _(k−1) b _(k−1)*, 1≦k≦M−1  (13)

Assuming that the aliasing is cancelled, the transfer function for theoutput is in accordance with Equation 14:

$\begin{matrix}{{T(z)} = {\frac{1}{M}{\sum\limits_{k = 0}^{M - 1}{{F_{k}(z)}{H_{k}(z)}}}}} & (14)\end{matrix}$

If the transfer function T(z) is linear phase, the filter will be freefrom phase distortion. This quality may be ensured by choosing:f _(k)(n)=h _(k)(N−n)  (15)or equivalently:F _(k)(z)=z ^(−N) {tilde over (H)} _(k)(z)  (16)where

-   -   {tilde over (H)}(z) is the conjugate pose of H(z);    -   * denotes the conjugation of the coefficients; and

Given the above-mentioned considerations, one example of the inventionprescribes:a _(k) =e ^(jθ(k))  (17)b _(k) =a _(k)*=e^(−jθ(k))  (18)c _(k) =W ^((k+0.5)N/2)  (19)where

-   -   θ(k)=(−1)^(k)π/4

It is therefore possible to derive:h _(k)(n)=2p ₀(n)cos(π/M(k+0.5)(n−N/2)+θ_(k))  (20)f _(k)(n)=2p ₀(n)cos(π/M(k+0.5)(n−N/2)−θ_(k))  (21)

Thus, the analysis filter (Equation 20), and the synthesis filterEquation 21), are related to the prototype p₀(n) by cosine modulation.

From the above-described requirements and with the aim of achievingperfect reconstruction, the condition on the prototype for perfectreconstruction can be derived A prototype derivation for the case N+1=2mM is provided by Vaiyanathan P. P., “Multirate Systems and FilterBanks”, Prentice Hall Signal Processing Series. 1992.

Where N+1=2 mM+m₁ the derivation is given by Nguyen T. Q. and KoilpillaiD., “The theory and design of arbitrary length cosine modulated filterbanks and wavelengths, satisfying perfect reconstruction”, IEEETransaction on Acoustic, Speech and Signal Processing, vol. ASSP-“44,pp. 473-483, 1996.

$\begin{matrix}{{{{{\overset{\sim}{G}}_{k}(z)}{G_{k}(z)}} + {{{\overset{\sim}{G}}_{M + k}(z)}{G_{M + k}(z)}}} = \frac{1}{2M}} & (22)\end{matrix}$

Equation 22 is known to those skilled in the art to represent thesufficient conditions of the polyphase components of a prototype forperfect reconstruction.

To obtain good frequency selectivity for each of the sub-bands, theprototype filter is designed as a lowpass prototype filter P₀(Z) withhigh stop band attenuation. The 2M polyphase components, G_(k)(z), mustalso satisfy the perfect reconstructions conditions of equation (22).

A method for designing a prototype which automatically satisfies theperfect reconstruction constraint of Equation (22) is through aParaunitary QMF Lattice structure described in Vaiyanathan P. P.,“Multirate Systems and Filter Banks”, Pentice Hall Signal ProcessingSeries. 1992. Here, the design method consists of optimizing rotationangles so that the stop band attenuation of the resulting prototypefilter is minimized. The optimization time can be prohibitive since thecost function (stop band attenuation) is a highly non-linear functionwith respect to the rotation angles.

Instead of optimizing in the rotation angle space, a design formulationwhich uses the filter coefficients directly is proposed by Nguyen T., “AQuadratic-Least Square approach to the design of digital filter banks”,International Symposium on Circuits and system, pp1344 to 1348, 1992. Inhis approach, the cost function and the perfect reconstruction conditionof Equation (22) are expressed as quadratic functions of the filtercoefficients. Since not all the constraint matrices arepositive-definite the minimization is still a difficult optimizationtheory (mathematical programming) problem. The approach recommended bythe author is based on linearizing of the quadratic constraint. Itresults in an approximate solution albeit the deviation from PR is verysmall.

In one example of the invention a unified MPEG-1 filter bank design withN+1=1632 and M=576. The polyphase components may be numerous (2M=1152),however, they are each of a low order. If the prototype filter isexpressed as vector h=[h₀ h₁ h₂ h₃ . . . h₁₆₃₁]^(t), then the polyphasecomponents can be represented as:G ₀(z)=h ₀ +h ₁₁₅₂ z ⁻¹G ₁(z)=h ₁ +h ₁₁₅₃ z ⁻¹G ₄₇₉(z)=h ₄₇₉ +h ₁₆₃₁ z ⁻¹G ₄₈₀(z)=h ₄₈₀G ₄₈₁(z)=h ₄₈₁G ₁₁₅₁(z)=h ₁₁₅₁

However, the fact that h_(n)=h_(1631−n), a symmetric property of linearphase filters, reduces the number of unknowns by half. For example,consider the perfect reconstruction condition for k=0:

$\begin{matrix}{{{{{\overset{\sim}{G}}_{0}(z)}{G_{0}(z)}} + {{{\overset{\sim}{G}}_{576}(z)}{G_{576}(z)}}} = \frac{1}{1152}} & (23)\end{matrix}$This translates to:(h ₀ +h ₁₁₅₂ z)(h ₀ +h ₁₁₅₂ z ⁻¹)+(h ₅₇₆)(h ₅₇₆)=h ² ₀ +h ₀ h ₁₁₅₂(z+z⁻¹)+h ² ₅₇₆=1  (24)

This implies that at least one of h₀ or h₁₁₅₂ must be zero. By choosinghost h₁₁₅₂=0 and h₀=a, h₅₇₆=√{square root over ((1−a²))}. Furthermore,due to symmetry:h ₁₀₅₅ =h ¹⁶³¹⁻¹⁰⁵⁵ =h ₅₇₆=√{square root over ((1−a ²))}  (25)

Also, h₁₆₃₁=h₀=a and h₄₇₉=h¹⁶³¹⁻⁴⁷⁹=h₁₁₅₂=0. From this we see that thenumber of unknowns is drastically reduced. This reduced set can beoptimized for minimum stop band energy.

Due to the simplicity of the polyphase components of in theabove-mentioned embodiments of the invention simplified constraintmapping can be performed.

In the above-mentioned examples of the invention, a FIR satisfying theperfect reconstruction constraint of Equation (22) and having reasonablefrequency selectivity can be obtained by modifying certain coefficientswhere minimal changes occur in the frequency response. Using advancedoptimization techniques (e.g. those based on Karsuch Kuhn Tucker'sTheorem) better solutions may be obtained.

1. An MPEG-1 CODEC, comprising: an encoder that includes means foreffecting an analysis filter bank, wherein the means for effecting theanalysis filter bank includes a unified filter bank; and a decoder thatincludes means for effecting a synthesis filter bank, wherein the meansfor effecting the synthesis filter bank includes a functional inverse ofthe unified filter bank, wherein the unified filter bank includes aplurality of audio signal filters, where each audio signal filter of theplurality of audio signal filters is a cosine modulation of a prototypefilter, P₀(Z), wherein the prototype filter includes a plurality ofpolyphase components, G_(k)(Z), which substantially satisfy thefollowing:${{{{\overset{\sim}{G}}_{k}(z)}{G_{k}(z)}} + {{{\overset{\sim}{G}}_{M + k}(z)}{G_{M + k}(z)}}} = \frac{1}{2M}$where G_(k)(z), for 0≦k≦M−1, are the polyphase components of theprototype filter; {tilde over (G)}_(k) (z) is a conjugate transpose ofG_(k)(z); M is a decimation factor of the prototype filter; and k is aninteger, wherein the MPEG-1 CODEC is a MPEG-1 Layer III CODEC wherein:the prototype filter has a temporal resolution, N, of substantiallyN+1=1632; the decimation factor, M, of the prototype filter issubstantially M=576; and the prototype filter has a bandwidth ofsubstantially π/M.
 2. The MPEG-1 CODEC claimed in claim 1, wherein theMPEG-1 CODEC functions substantially in accordance with the followingtransfer function:${{T(Z)} = {\frac{1}{M}{\sum\limits_{k = 0}^{M - 1}{{F_{k}(Z)}{H_{k}(Z)}}}}};$h_(k)(n) = 2p₀(n)cos (π/M(k + 0.5)(n − N/2) + θ_(k));f_(k)(n) = 2p₀(n)cos (π/M(k + 0.5)(n − N/2) + θ_(k)); and${{F_{k}(z)} = {z^{- N}{{\overset{\sim}{H}}_{k}(z)}}};$ where: H_(k)(Z)is a k^(th) filter of the analysis filter bank; F_(k)(Z) is a k^(th)filter of the synthesis filter bank; {tilde over (H)}_(k)(z) is aconjugate transpose of H_(k)(z); M is a decimation factor of the unifiedfilter; and N is a temporal resolution of the prototype filter.
 3. TheMPEG-1 CODEC claimed in claim 1, wherein the MPEG-1 CODEC functionssubstantially in accordance with the following transfer function:${{T(Z)} = {\frac{1}{M}{\sum\limits_{k = 0}^{M - 1}{{F_{k}(Z)}{H_{k}(Z)}}}}};$H_(k)(z) = a_(k)c_(k)P₀(z W^(k + 0.5)) + a_(k)^(*)c_(k)^(*)P₀(z W^(−(k + 0.5))), 0 ≤ k ≤ M − 1;F_(k)(z) = b_(k)c_(k)P₀(z W^(k + 0.5)) + b_(k)^(*)c_(k)^(*)P₀(z W^(−(k + 0.5))), 0 ≤ k ≤ M − 1; and${{F_{k}(z)} = {z^{- N}{{\overset{\sim}{H}}_{k}(z)}}};$ Where: H_(k)(Z)is a k^(th) filter of the analysis filter bank; F_(k)(z) is a k^(th)filter of the synthesis filter bank; {tilde over (H)}_(k)(z) is aconjugate transpose of H_(k)(z); {tilde over (G)}_(k)(z) is a conjugatetranspose of G_(k)(z); M is a decimation factor of the unified filter,a_(k), b_(k) and c_(k) are unit magnitude constants, wherein:a _(k) b _(k) *=−a _(k−1) b _(k−1)*, 1≦k≦M−1;a _(k) =e ^(jθ(k));b _(k) =a _(k) *=e ^(−jθ(k));c _(k) =W ⁽ k+0.5) N/2; and wherein θ(k)=(−1)^(k)π/4; * denotes aconjugation of respective coefficients; andW=W _(2M)=e^(−j2π/2M).
 4. The MPEG-1 CODEC claimed in claim 1, whereinthe prototype filter can be expressed as a vector h=[h₁ h₂ h₃ . . .h₁₆₃₁]^(t) and the polyphase components, G_(k)(z), of the prototypefilter are:G ₀(z)=h ₀ +h ₁₁₅₂ z ⁻¹G ₁(z)=h ₁ +h ₁₁₅₃ z ⁻¹G ₄₇₉(z)=h ₄₇₉ +h ₁₆₃₁ z ⁻¹G ₄₈₀(z)=h ₄₈₀G ₄₈₁(z)=h ₄₈₁G ₁₁₅₁(z)=h ₁₁₅₁.
 5. The MPEG-1 CODEC claimed in claim 1, wherein saidprototype filter is designed through a paraunitary Quadrature MirrorFilter Lattice structure.
 6. A method for encoding and decoding audiodata in a MPEG-1 Layer III CODEC that includes a unified filter bank,having an analysis filter bank, and synthesis filter bank that is afunctional inverse of the unified filter bank, the method comprising:encoding input audio data into coded audio data, the encoding stepincluding subjecting the input audio data to the analysis filter bank;and decoding the coded audio data into output audio data, the decodingstep including subjecting the coded audio data to the synthesis filterbank, the unified filter bank including a plurality of filters, whereeach filter of the plurality of filters is a cosine modulation of aprototype filter, P₀(Z), wherein: the prototype filter has a temporalresolution, N, of substantially N+1=1632; the prototype filter has adecimation factor, M, of substantially M=576; the prototype filter has abandwidth of substantially π/M; and the prototype filter substantiallysatisfies the following constraint:${{{{\overset{\sim}{G}}_{k}(z)}{G_{k}(z)}} + {{{\overset{\sim}{G}}_{M + k}(z)}{G_{M + k}(z)}}} = \frac{1}{2M}$where, G_(k)(z), for 0≦k≦M−1 are polyphase components of the prototypefilter; {tilde over (G)}_(k)(z) is a conjugate transpose of G_(k)(z);and k is an integer.
 7. The method claimed in claim 6, wherein theMPEG-1 Layer III CODEC functions substantially in accordance with thefollowing transfer function:${{T(Z)} = {\frac{1}{M}{\sum\limits_{k = 0}^{M - 1}{{F_{k}(Z)}{H_{k}(Z)}}}}};$h_(k)(n) = 2p₀(n)cos (π/M(k + 0.5)(n − N/2) + θ_(k));f_(k)(n) = 2p₀(n)cos (π/M(k + 0.5)(n − N/2) + θ_(k)); and${{F_{k}(z)} = {z^{- N}{{\overset{\sim}{H}}_{k}(z)}}};$ where: H_(k)(Z)is a k^(th) filter of the analysis filter bank; F_(k)(Z) is a k^(th)filter of the synthesis filter bank; {tilde over (H)}_(k)(z) is aconjugate transpose of H_(k)(z); M is a decimation factor of the unifiedfilter; and N is a temporal resolution of the prototype filter.
 8. Themethod claimed in claimed 6, wherein the MPEG-1 Layer III CODECfunctions substantially in accordance with the following transferfunction:${{T(Z)} = {\frac{1}{M}{\sum\limits_{k = 0}^{M - 1}{{F_{k}(Z)}{H_{k}(Z)}}}}};$H_(k)(z) = a_(k)c_(k)P₀(z W^(k + 0.5)) + a_(k)^(*)c_(k)^(*)P₀(z W^(−(k + 0.5))), 0 ≤ k ≤ M − 1;F_(k)(z) = b_(k)c_(k)P₀(z W^(k + 0.5)) + b_(k)^(*)c_(k)^(*)P₀(z W^(−(k + 0.5))), 0 ≤ k ≤ M − 1; and${{F_{k}(z)} = {z^{- N}{{\overset{\sim}{H}}_{k}(z)}}};$ where: H_(k)(Z)is a k^(th) filter of the analysis filter bank; F_(k)(Z) is a k^(th)filter of the synthesis filter bank; {tilde over (H)}_(k)(z) is aconjugate transpose of H_(k)(z); {tilde over (G)}_(k)(z) is a conjugatetranspose of G_(k)(z); M is a decimation factor of the unified filter,a_(k), b_(k) and c_(k) are unit magnitude constants, wherein:a _(k) b _(k) * =−a _(k−1) b _(k−1)* , 1≦k≦M−1;a _(k) =e ^(jθ(k));b _(k) =a _(k) *=e ^(−jθ(k));c _(k) =W ^((k−0.5)N/2); and wherein θ(k)=(−1)^(k)π/4; * denotes aconjugation of respective coefficients; andW=W _(2M) =e ^(−j2π/2M).
 9. The method claimed in claim 6, wherein saidprototype filter can be expressed as a vector h=[h₁ h₂ h₃ . . .h₁₆₃₁]^(t) and the polyphase components, G_(k)(Z), of the prototypefilter are:G ₀(z)=h ₀ +h ₁₁₅₂ z ⁻¹G ₁(z)=h ₁ +h ₁₁₅₃ z ⁻¹G ₄₇₉(z)=h ₄₇₉ +h ₁₆₃₁ z ⁻¹G ₄₈₀(z)=h ₄₈₀G ₄₈₁(z)=h ₄₈₁G ₁₁₅₁(z)=h ₁₁₅₁.
 10. The method claimed in claim 6, wherein saidprototype filter is designed through a paraunitary Quadrature MirrorFilter Lattice structure.
 11. The method claimed in claim 6, wherein theunified filter bank has a spectral resolution and frequency selectivityof a MPEG-1 Layer III hybrid analysis filter.
 12. An MPEG CODEC,comprising: an encoder that includes a unified filter bank having aplurality of audio signal filters; and a decoder that includes asynthesis filter bank that is a functional inverse of the unified filterbank, wherein the unified filter bank and synthesis filter bank arestructured to provide the MPEG CODEC with the following transferfunction:${{T(Z)} = {\frac{1}{M}{\sum\limits_{k = 0}^{M - 1}{{F_{k}(Z)}{H_{k}(Z)}}}}};$H_(k)(z) = a_(k)c_(k)P₀(z W^(k + 0.5)) + a_(k)^(*)c_(k)^(*)P₀(z W^(−(k + 0.5))), 0 ≤ k ≤ M − 1;F_(k)(z) = b_(k)c_(k)P₀(z W^(k + 0.5)) + b_(k)^(*)c_(k)^(*)P₀(z W^(−(k + 0.5))), 0 ≤ k ≤ M − 1; and${{F_{k}(z)} = {z^{- N}{{\overset{\sim}{H}}_{k}(z)}}};$ where: H_(k)(z)is a k^(th) filter of the analysis filter bank; F_(k)(z) is a k^(th)filter of the synthesis filter bank; {tilde over (H)}_(k)(z) is aconjugate transpose of H_(k)(z); {tilde over (G)}_(k)(z) is a conjugatetranspose of G_(k)(z); M is a decimation factor of the unified filter;a_(k), b_(k) and c_(k) are unit magnitude constants; * denotes aconjugation of respective coefficients; and W=W_(2M)=e^(−j2π/2M),wherein where each audio signal filter of the plurality of audio signalfilters is a cosine modulation of a prototype filter, P₀(Z), wherein theprototype filter includes a plurality of polyphase components, G_(k)(Z),which substantially satisfy the following:${{{{\overset{\sim}{G}}_{k}(z)}{G_{k}(z)}} + {{{\overset{\sim}{G}}_{M + k}(z)}{G_{M + k}(z)}}} = \frac{1}{2M}$where G_(k)(z), for 0≦k≦M−1, are the polyphase components of theprototype filter; {tilde over (G)}_(k)(z) is a conjugate transpose ofG_(k)(z); M is a decimation factor of the prototype filter; and k is aninteger, wherein the MPEG CODEC is a MPEG-1 Layer III CODEC wherein: theprototype filter has a temporal resolution, N, of substantiallyN+1=1632; the decimation factor, M, of the prototype filter issubstantially M =576; and the prototype filter has a bandwidth ofsubstantially π/M.
 13. The MPEG CODEC of claim 12 wherein the prototypefilter can be expressed as a vector h =[h₁ h₂ h₃ . . . h₁₆₃₁]^(t) andthe polyphase components, G_(k)(z), of the prototype filter are:G ₀(z)=h ₀ +h ₁₁₅₂ z ⁻¹G ₁(z)=h ₁ +h ₁₁₅₃ z ⁻¹G ₄₇₉(z)=h ₄₇₉ +h ₁₆₃₁ z ⁻¹G ₄₈₀(z)=h ₄₈₀G ₄₈₁(z)=h ₄₈₁G ₁₁₅₁(z)=h ₁₁₅₁.
 14. The MPEG CODEC of claim 12 wherein said prototypefilter is designed through a paraunitary Quadrature Mirror FilterLattice structure.
 15. The MPEG CODEC of claim 12, wherein:a _(k) b _(k) *=−a _(k−1) b _(k−1)*, 1≦k≦M−1;a _(k) =e ^(jθ(k));b _(k) =a _(k) *=e ^(−jθ(k));c _(k) =W ^((k+0.5)N/2; and)θ(k)=(−1)^(k)π/4.
 16. The MPEG CODEC of claim 12, wherein the unifiedfilter bank has a spectral resolution and frequency selectivity of aMPEG-1 Layer III hybrid analysis filter.
 17. An MPEG-1 CODEC,comprising: an encoder that includes means for effecting an analysisfilter bank; wherein the means for effecting the analysis filter bankincludes a unified filter bank; and a decoder that includes means foreffecting a synthesis filter bank, wherein the means for effecting thesynthesis filter bank includes a functional inverse of the unifiedfilter bank, wherein the unified filter bank includes a plurality ofaudio signal filters, where each audio signal filter of the plurality ofaudio signal filters is a cosine modulation of a prototype filter,P₀(Z), wherein the prototype filter includes a plurality of polyphasecomponents, G_(k)(Z), which substantially satisfy the following:${{{{\overset{\sim}{G}}_{k}(z)}{G_{k}(z)}} + {{{\overset{\sim}{G}}_{M + k}(z)}{G_{M + k}(z)}}} = \frac{1}{2M}$where G_(k)(z), for 0≦k≦M−1, are the polyphase components of theprototype filter; {tilde over (G)}_(k)(z) is a conjugate transpose ofG_(k)(z); M is a decimation factor of the prototype filter; and k is aninteger, wherein the prototype filter can be expressed as a vector h=[h₁ h₂ h₃ . . . h₁₆₃₁]^(t) and the polyphase components, G_(k)(z), ofthe prototype filter are:G ₀(z)=h ₀ +h ₁₁₅₂ z ⁻¹G ₁(z)=h ₁ +h ₁₁₅₃ z ⁻¹G ₄₇₉(z)=h ₄₇₉ +h ₁₆₃₁ z ⁻¹G ₄₈₀(z)=h ₄₈₀G ₄₈₁(z)=h ₄₈₁G ₁₁₅₁(z)=h ₁₁₅₁.
 18. The MPEG-1 CODEC claimed in claim 17, wherein theMPEG-1 CODEC functions substantially in accordance with the followingtransfer function:${{T(Z)} = {\frac{1}{M}{\sum\limits_{k = 0}^{M - 1}{{F_{k}(Z)}{H_{k}(Z)}}}}};$h_(k)(n) = 2p₀(n)cos (π/M(k + 0.5)(n − N/2) + θ_(k));f_(k)(n) = 2p₀(n)cos (π/M(k + 0.5)(n − N/2) + θ_(k)); and${{F_{k}(z)} = {z^{- N}{{\overset{\sim}{H}}_{k}(z)}}};$ where: H_(k)(Z)is a k^(th) filter of the analysis filter bank; F_(k)(Z) is a k^(th)filter of the synthesis filter bank; {tilde over (H)}_(k)(z) is aconjugate transpose of H_(k)(z); M is a decimation factor of the unifiedfilter; and N is a temporal resolution of the prototype filter.
 19. TheMPEG-1 CODEC claimed in claim 17, wherein the MPEG-1 CODEC functionssubstantially in accordance with the following transfer function:${{T(Z)} = {\frac{1}{M}{\sum\limits_{k = 0}^{M - 1}{{F_{k}(Z)}{H_{k}(Z)}}}}};$H_(k)(z) = a_(k)c_(k)P₀(z W^(k + 0.5)) + a_(k)^(*)c_(k)^(*)P₀(z W^(−(k + 0.5))), 0 ≤ k ≤ M − 1;F_(k)(z) = b_(k)c_(k)P₀(z W^(k + 0.5)) + b_(k)^(*)c_(k)^(*)P₀(z W^(−(k + 0.5))), 0 ≤ k ≤ M − 1; and${{F_{k}(z)} = {z^{- N}{{\overset{\sim}{H}}_{k}(z)}}};$ Where: H_(k)(Z)is a k^(th) filter of the analysis filter bank; F_(k)(Z) is a k^(th)filter of the synthesis filter bank; {tilde over (H)}_(k)(z) is aconjugate transpose of H_(k)(z); {tilde over (G)}_(k)(z) is a conjugatetranspose of G_(k)(z); M is a decimation factor of the unified filter,a_(k), b_(k) and c_(k) are unit magnitude constants, wherein:a _(k) b _(k) *=−a _(k−1) b _(k−1)*, 1≦k≦M−1;a_(k)=e^(jθ(k));b_(k)=a_(k)*=e^(−jθ(k));c_(k)=W^((k+0.5)N/2); and wherein θ(k)=(−1)^(k)π/4; * denotes aconjugation of respective coefficients; andW=W_(2M)=e^(−2π/2M).
 20. The MPEG-1 CODEC claimed in claim 17, whereinsaid prototype filter is designed through a paraunitary QuadratureMirror Filter Lattice structure.
 21. An MPEG CODEC, comprising: anencoder that includes a unified filter bank having a plurality of audiosignal filters; and a decoder that includes a synthesis filter bank thatis a functional inverse of the unified filter bank, wherein the unifiedfilter bank and synthesis filter bank are structured to provide the MPEGCODEC with the following transfer function:${{T(Z)} = {\frac{1}{M}{\sum\limits_{k = 0}^{M - 1}{{F_{k}(Z)}{H_{k}(Z)}}}}};$H_(k)(z) = a_(k)c_(k)P₀(z W^(k + 0.5)) + a_(k)^(*)c_(k)^(*)P₀(z W^(−(k + 0.5))), 0 ≤ k ≤ M − 1;F_(k)(z) = b_(k)c_(k)P₀(z W^(k + 0.5)) + b_(k)^(*)c_(k)^(*)P₀(z W^(−(k + 0.5))), 0 ≤ k ≤ M − 1; and${{F_{k}(z)} = {z^{- N}{{\overset{\sim}{H}}_{k}(z)}}};$ where: H_(k)(z)is a k^(th) filter of the analysis filter bank; F_(k)(Z) is a k^(th)filter of the synthesis filter bank; {tilde over (H)}_(k)(z) is aconjugate transpose of H_(k)(z); {tilde over (G)}_(k)(z) is a conjugatetranspose of G_(k)(z); M is a decimation factor of the unified filter;a_(k), b_(k) and c_(k) are unit magnitude constants; * denotes aconjugation of respective coefficients; and W =W_(2M)=e^(−2π/2M),wherein where each audio signal filter of the plurality of audio signalfilters is a cosine modulation of a prototype filter, P₀(Z), wherein theprototype filter includes a plurality of polyphase components, G_(k)(Z),which substantially satisfy the following:${{{{\overset{\sim}{G}}_{k}(z)}{G_{k}(z)}} + {{{\overset{\sim}{G}}_{M + k}(z)}{G_{M + k}(z)}}} = \frac{1}{2M}$where G_(k)(z), for 0≦k≦M−1, are the polyphase components of theprototype filter; {tilde over (G)}_(k)(z) is a conjugate transpose ofG_(k)(z); M is a decimation factor of the prototype filter; and k is aninteger, wherein the prototype filter can be expressed as a vector h=[h₁ h₂ h₃ . . . h₁₆₃₁]^(t) and the polyphase components, G_(k)(Z), ofthe prototype filter are:G ₀(z)=h ₀ +h ₁₁₅₂ z ⁻¹G ₁(z)=h ₁ +h ₁₁₅₃ z ⁻¹G ₄₇₉(z)=h ₄₇₉ +h ₁₆₃₁ z ⁻¹G ₄₈₀(z)=h ₄₈₀G ₄₈₁(z)=h ₄₈₁G ₁₁₅₁(z)=h _(1151.)
 22. The MPEG CODEC of claim 21, wherein saidprototype filter is designed through a paraunitary Quadrature MirrorFilter Lattice structure.
 23. The MPEG CODE C of claim 21, wherein:a _(k) b _(k) * =−a _(k−1) b _(k−1)*, 1≦k≦M−1a _(k)=e^(jθ(k));b _(k) =a _(k)*=e^(−jθ(k));c _(k)=W^((k+0.5)N/2); andθ(k)=(−1)^(k)π/4.